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Exam 3: Confidence Intervals

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Question 21

True/False

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Use the following to answer the questions below: Identify if each of the following statements is a proper interpretation of a 95% confidence interval. -The probability that the population parameter is in this interval is 0.95.

A) True
B) False

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Question 22

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Use the following to answer the questions below: There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university. -Suppose another class does the same in class exercise and gets a 95% confidence interval of -0.86 to 5.34 for the difference in the mean number of hours spent watching television for males and females at this university. Interpret this 95% confidence interval in the context of this data situation.

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We are 95% sure that the diffe...

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Question 23

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Use the following to answer the questions below: Suppose that a 95% confidence interval for the slope of a regression line based on a sample of size n = 100 and the percentiles of the slopes for 1,000 bootstrap samples goes from 2.50 to 2.80. For each change described (with all else staying the same) , indicate which of the three confidence intervals would be the most likely result. -Increase the number of bootstrap samples to 5,000.

Use the following to answer the questions below: In a recent Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over) , 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. They also report that the "margin of sampling error is plus or minus 4%." -What is the sample being used?

Use the following to answer the following questions: A study to investigate the dominant paws in cats was described in the scientific journal Animal Behaviour. The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed." -Use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error. A) SE = 0.078 B) SE = 0.042 C) SE = 0.156 D) SE = 0.636

Use the following to answer the following questions: A study to investigate the dominant paws in cats was described in the scientific journal Animal Behaviour. The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed." -Suppose you estimate of the standard error to be 0.056. Construct a 95% confidence interval for the proportion of domestic cats that are "left-pawed". Round the margin of error to three decimal places. A) 0.364 to 0.588 B) 0.420 to 0.532 C) 0.392 to 0.560 D) 0.402 to 0.550

Use the following to answer the questions below: In a survey conducted by the Gallup organization, 1,017 adults were asked, "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all." -Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

A bootstrap distribution will be centered at the value of the original statistic.

Use the following to answer the questions below: A study to investigate the dominant paws in cats was described in the scientific journal Animal Behaviour. The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed." -A bootstrap distribution, based on 1,000 bootstrap samples is provided. Use the distribution to estimate a 99% confidence interval for the population mean. Explain how you arrived at your answer.

Use the following to answer the questions below: A study to investigate the dominant paws in cats was described in the scientific journal Animal Behaviour. The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna) , and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days) . The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous") . Of the 42 cats studied, 20 were classified as "left-pawed." -Where should the bootstrap distribution be centered?

Use the following to answer the questions below: The sampling distribution shows sample means from samples of size n = 50. ‪ -Using the sampling distribution, how likely is = 68.7?

Use the following to answer the questions below: In a survey conducted by the Gallup organization, 1,017 adults were asked, "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all." -Use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error.

Use the following to answer the questions below: The sampling distribution shows sample proportions from samples of size n = 35. ‪ -Using the sampling distribution, how likely is = 0.45?

Use the following to answer the questions below: There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university. ‪ -Where should the bootstrap distribution be centered?

Use the following to answer the questions below: An Internet provider contacts a random sample of 300 customers and asks how many hours per week the customers use the Internet. It found the average amount of time spent on the Internet per week to be about 7.2 hours. -Percentiles of the bootstrap distribution are provided. Use the percentiles to report a 90% confidence interval for the parameter.

Use the following to answer the questions below: Identify each of the following as either a parameter or a statistic, and give the correct notation. -Correlation between height and armspan (distance from fingertip to fingertip when arms are extended to the sides) for all players on the Chicago Bulls basketball team, using data from all players currently on the team

Use the following to answer the questions below: There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university. -Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Use the following to answer the questions below: Suppose we are interested in comparing the proportion of male students who smoke to the proportion of female students who smoke. We have a random sample of 150 students (60 males and 90 females) that includes two variables: Smoke = "yes" or "no" and Gender = "female (F) " or "male (M) ." The two-way table below summarizes the results. -Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles to provide a 98% confidence interval for the difference in the proportion of smokers between male and female students.

Use the following to answer the following questions: A study to investigate the dominant paws in cats was described in the scientific journal Animal Behaviour. The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed." -Use the data from the sample to estimate the parameter of interest. Report your answer with three decimal places.

Use the following to answer the questions below: In a survey conducted by the Gallup organization, 1,017 adults were asked, "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all." -Use the estimate of the standard error to construct a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Round the margin of error to three decimal places.